On a random walk with memory and its relation to Markovian processes

Details On a random walk with memory and its relation to Markovian processes On a random walk with memory and its relation to Markovian processes

2010-05-21

arxiv.org/abs/1005.3896v1

J. Phys. A, 43 (2010) 285006

Physics

Condensed Matter

Statistical Mechanics

10 pages, 4 figures

Scientific paper

10.1088/1751-8113/43/28/285006

We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk. The time evolution of the displacement is given by an equivalent Markovian dynamical process. The probability density for the position of the walker is the same at any time as for a random walk with shrinking steps, although the two-time correlation functions are quite different.

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